Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series B, Pt. 1, pp. 57--75



S. E. AHMED, University of Regina

SUMMARY.  The problem of estimating the coefficient of variation is considered when it is a priori suspected that two coefficients of variations are the same. It is advantageous to pool the data for making inferences about population coefficient of variation. The estimators based on pre-test and the shrinkage principle are proposed. The expressions for the asymptotic bias and asymptotic mean-square error (AMSE) of the proposed estimators are derived and compared with the parallel expressions for the unrestricted and pooled estimators. Interestingly, the proposed estimator dominates the unrestricted estimator in a wider range. Not only that, the size for the preliminary test is also appropriate. Furthermore, an optimal rule for the choice of the level of significance ($\alpha$) for the preliminary test is presented. Tables for the optimum selection of  $\alpha$ is also provided for the use of the shrinkage preliminary test estimator.

AMS (1990) subject classification.  62F10.

Key words and phrases. Shrinkage restricted estimator, shrinkage preliminary test estimator, asymptotic biases and risks, asymptotic efficiency.

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